MILP-Based Short-Term Thermal Unit Commitment and Hydrothermal Scheduling Including Cascaded Reservoirs and Fuel Constraints

Reservoirs are often built in cascade on the same river system, introducing inexorable constraints. It is therefore strategically important to scheme out an efficient commitment of thermal generation units along with the scheduling of hydro generation units for better operational efficiency, considering practical system conditions. This paper develops a comprehensive, unit-wise hydraulic model with reservoir and river system constraints, as well as gas constraints, with head effects, to commit thermal generation units and schedule hydro ones in the short-term. A mixed integer linear programming (MILP) methodology, using the branch and bound & cut (BB&C) algorithm, is employed to solve the resultant problem. Due to the detailed modelling of individual hydro units and cascaded dependent reservoirs, the problem size is substantially swollen. Multithread computing is invoked to accelerate the solution process. Simulation results, conducted on various test systems, reiterate that the developed MILP-based hydrothermal scheduling approach outperforms other techniques in terms of cost efficiency

Solving Stochastic Hydrothermal Unit Commitment with a New Primal Recovery Technique Based on Lagrangian Solutions

The high penetration of intermittent renewable generation has prompted the development of Stochastic Hydrothermal Unit Commitment (SHUC) models, which are more difficult to be solved than their thermal-based counterparts due to hydro generation constraints and inflow uncertainties. This work presents a SHUC model applied in centralized cost-based dispatch. The SHUC is represented by a two-stage stochastic model, formulated as a large-scale mixed-binary linear programming problem. The solution strategy is divided into two steps. The first step is the Lagrangian Relaxation (LR) approach, which is applied to solve the dual problem and generate a lower bound for SHUC. The second step is given by a Primal Recovery where we use the solution of the LR dual problem with heuristics based on Benders’ Decomposition to obtain the primal-feasible solution. Both steps benefit from each other, exchanging information over the iterative process. We assess our approach in terms of the quality of the solutions and running times on space and scenario LR decompositions. The computational instances use various power systems, considering the different configuration of plants (capacity and number of units). The results show the advantage of our primal recovery technique compared to solving the problem via MILP solver. This is true already for the deterministic case, and the advantage grows as the problem’s size (number of plants and/or scenarios) does. The space decomposition provides better solutions, although scenario one provides better lower bounds, but the main idea is to encourage researchers to explore LR decompositions and heuristics in other relevant problems

Solving Stochastic Hydrothermal Unit Commitment with a New Primal RecoverycTechnique Based on Lagrangian Solutions

The high penetration of intermittent renewable generation has prompted the development of Stochastic Hydrothermal Unit Commitmentc(SHUC) models, which are more difficult to be solved than their thermal-basedccounterparts due to hydro generation constraints and inflow uncertainties.cThis work presents a SHUC model applied in centralized cost-based dispatch, where the uncertainty is related to the water availability in reservoirs and demand. The SHUC is represented by a two-stage stochastic model, formulated as a large-scale mixed-binary linear programming problem. The solution strategy is divided into two steps, performed sequentially, with intercalated iterations to find the optimal generation schedule. The first step is the Lagrangian Relaxation (LR) approach. The second step is given by a Primal Recovery based on LR solutions and a heuristic based on Benders' Decomposition. Both steps benefit from each other, exchanging information over the iterative process. We assess our approach in terms of the quality of the solutions and running times on space and scenario LR decompositions. The results show the advantage of our primal recovery technique compared to solving the problem via MILP solver. This is true already for the deterministic case, and the advantage grows as the problem’s size (number of plants and/or scenarios) does

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Hydrothermal Unit Commitment with Deterministic Optimization: Generation and Transmission Including Pumped Storage Units

This work presents a novel approach for solving the short-therm scheduling of hydro-thermal power generation, including pumped storage systemsand transmission constraints. The problem addressed is known as Security Constrained Unit Commitment (SCUC). Pumped Storage Units (PSUs) are importantin electric systems during the off-peak and the peak demand periods, providing economic and technical benefits. Linear aproximations are applied to nonlinear equations of this kind of mathematical problems which are: fuel cost functions, generation-discharge curves of PSUs and transmission constraints modeled with Alternating Current power flow model. Thus, MILP models are presented for the problem addessed. To prove the efficiency of the proposed models, two systems with PSUs will be tested: a modified 6-bus and the IEEE 31-bus power system. Results show that the proposed MILP models allow: modeling the SCUC problem more realistically, obtaining feasible solutions within efficient computational times, and reaching production cost savings up to almost 20% compared to power systems that lack capacities to pumping water. Several indicators obtained from results are presented through graphs, as a tool for improving operation and maintenance of power systems. The analysis of these indicators and the graphic interpretation allow to identify and classify critical parts of systems as well as to make recommendations about future system improvements.Fil: Alvarez, Gonzalo Exequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Marcovecchio, Marian Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; ArgentinaFil: Aguirre, Pio Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo y Diseño. Universidad Tecnológica Nacional. Facultad Regional Santa Fe. Instituto de Desarrollo y Diseño; Argentin

A long-term unit commitment problem with hydrothermal coordination for economic and emission control in large-scale electricity systems

The paper describes a long-term scheduling problem for thermal power plants and energy storages. In addition, renewable energy sources are integrated by considering the residual demand. Besides the classical minimization of the production costs, emission-related costs are taken into account. Thereby, emission costs are determined by market prices for CO2 emission certificates (i.e., using the EU emissions trading system). For the proposed unit commitment problem with hydrothermal coordination for economic and emission control, an enhanced mixed-integer linear programming model is presented. Moreover, a new heuristic approach is developed, which consists of two solution stages. The heuristic first performs an isolated dispatching of thermal plants. Then, a re-optimization stage is included in order to embed activities of energy storages into the final solution schedule. The considered approach is able to find outstanding schedules for benchmark instances with a planning horizon of up to one year. Furthermore, promising results are also obtained for large-scale real-world electricity systems. For the German electricity market, the relationship of CO2 certificate prices and the optimal thermal dispatch is illustrated by a comprehensive sensitivity analysis

Optimization of Scheduling for Hydro-thermal Power Generation and Transmission Including Pumped Storage Systems

This work presents a novel approach for solving the short-term scheduling of hydro-thermal power generation, including pumped storage systems and transmission constraints. The problem addressed is known as Security Constrained Unit Commitment (SCUC). Pumped Storage Units (PSUs) are important in electric systems during the off-peak and the peak demand periods, providing economic and technical benefits. Linear aproximations are applied to nonlinear equations of this kind of mathematical problems which are: fuel cost functions, generation-discharge curves of PSUs and transmission constraints modeled with Alternating Current power flow model. Thus, MILP models are presented for the problem addessed. To prove the efficiency of the proposed models, two systems with PSUs will be tested: a modified 6-bus and the IEEE 31-bus power system. Results show that the proposed MILP models allow: modeling the SCUC problem more realistically, obtaining feasible solutions within efficient computational times, and reaching production cost savings up to almost 15% compared to power systems that lack capacities to pumping water. Several indicators obtained from results are presented through graphs, as a tool for improving operation and maintenance of power systems. The analysis of these indicators and the graphic interpretation allow to identify and classify critical parts of systems as well as to make recommendations about future system improvements.Sociedad Argentina de Informática e Investigación Operativ

Unit Commitment Problem in Electrical Power System: A Literature Review

Unit commitment (UC) is a popular problem in electric power system that aims at minimizing the total cost of power generation in a specific period, by defining an adequate scheduling of the generating units. The UC solution must respect many operational constraints. In the past half century, there was several researches treated the UC problem. Many works have proposed new formulations to the UC problem, others have offered several methodologies and techniques to solve the problem. This paper gives a literature review of UC problem, its mathematical formulation, methods for solving it and Different approaches developed for addressing renewable energy effects and uncertainties

Optimization of Scheduling for Hydro-thermal Power Generation and Transmission Including Pumped Storage Systems

This work presents a novel approach for solving the short-term scheduling of hydro-thermal power generation, including pumped storage systems and transmission constraints. The problem addressed is known as Security Constrained Unit Commitment (SCUC). Pumped Storage Units (PSUs) are important in electric systems during the off-peak and the peak demand periods, providing economic and technical benefits. Linear aproximations are applied to nonlinear equations of this kind of mathematical problems which are: fuel cost functions, generation-discharge curves of PSUs and transmission constraints modeled with Alternating Current power flow model. Thus, MILP models are presented for the problem addessed. To prove the efficiency of the proposed models, two systems with PSUs will be tested: a modified 6-bus and the IEEE 31-bus power system. Results show that the proposed MILP models allow: modeling the SCUC problem more realistically, obtaining feasible solutions within efficient computational times, and reaching production cost savings up to almost 15% compared to power systems that lack capacities to pumping water. Several indicators obtained from results are presented through graphs, as a tool for improving operation and maintenance of power systems. The analysis of these indicators and the graphic interpretation allow to identify and classify critical parts of systems as well as to make recommendations about future system improvements.Sociedad Argentina de Informática e Investigación Operativ